yes, the dyes in lower end dog food like kibbles and bits will affect stool color.
please don’t feed a medium breed dog puppy food for small breeds. the nutrient amounts are incorrect for your puppy and can cause health problems. try to feed something that has no corn and has meat for the first two or three ingredients.
i would also wonder why you have a puppy 2 weeks early. puppies should not leave their mother and littermates prior to 8 weeks of age. is there any way you can take your puppy back to the breeder for 2 more weeks?
first: THANK YOU for linking to videos in your post. i really appreciate that, and it makes it a LOT easier to diagnose.
for 1 – i agree with you. i think she’s focusing on the “prey” with her odd head movement. i’ve seen this before in a healthy cat.
for 2 – maybe? i’d wait and see on it, honestly. if this is only during walks and play it may be behavior-related rather than health.